What the Data Shows

You need: a 30 cm ruler · a partner · a recording table

1. Your partner holds the ruler at the 30 cm end so the 0 cm mark hangs level with the top of your open thumb and finger.
2. Without warning, your partner lets go. Catch it as fast as you can.
3. Record the centimetre mark just above your thumb. A smaller number means a faster reaction.
4. Do five catches with your writing hand and five with your other hand. Record every result.
5. Find each person's median catch for each hand, then make two dot plots on the same scale for the class.

How you'll know: You can say which hand tends to be faster for the class, by about how many centimetres, and whether the two dot plots overlap a lot or a little.

Go further: Test after a minute of star jumps, or with a distraction. Keep everything else the same so the comparison is fair.

You need: stopwatch or phone timer · recording sheet

1. Close your eyes. Your partner says 'go' and starts the stopwatch; you say 'stop' when you think one minute has passed.
2. Record the real time in seconds. Swap roles.
3. Collect the whole class's times and draw a dot plot with a line at 60 seconds.
4. Calculate the mean, median and range.

How you'll know: Your summary says whether the class tends to guess short or long and by how much, using the median.

Go further: Compare counting in your head with not counting. Which group has the smaller range?

You need: a picture key of common NZ garden birds · clipboard and pencil · watch or timer · binoculars if you have them

1. Choose two spots: for example the open field and a planted garden or bush edge.
2. Sit quietly at the first spot for ten minutes. For each kind of bird, record the most you see at one time (so you don't count the same bird twice).
3. Repeat at the second spot at the same time of day, on a day with similar weather.
4. Make a clustered bar graph with both spots side by side.
5. Calculate the percentage of birds at each spot that were native.

How you'll know: Your graph lets someone see at a glance which spot had more birds and more native birds, and your percentages back it up.

Safety: Stay where the teacher can see you, wear a hat and sunscreen, and never approach or touch a nest.

Go further: Compare your counts with national results from the NZ Garden Bird Survey. Is your school typical?

You need: a clear straight-sided plastic bottle · a ruler · a few stones · tape · a recording sheet

1. An adult cuts the top off the bottle. Turn the top upside down into the bottle to make a funnel and tape it in place.
2. Put stones in the bottom, add water up to a line, and tape a ruler to the side with 0 at that line.
3. Place it in the open, away from roofs and trees, and read it at the same time every school day. Tip it back to the line after each reading.
4. Log two weeks of readings, and add NIWA or MetService readings for weekends and holidays.
5. Draw a time-series graph (days along the bottom, millimetres of rain up the side).

How you'll know: Your time-series graph shows wet and dry spells clearly, and you can say which day had the most rain and what the typical daily rainfall was.

Safety: An adult cuts the bottle; cut plastic edges are sharp. Tape over the cut edge.

Go further: Compare your gauge's readings with the nearest official weather station. How close are they, and why might they differ?

You need: two or three graphs from news sites, adverts or sports coverage (printed) · coloured pens · squared paper

1. For each graph, check for a title, axis labels, units, a scale that starts at zero (for bar graphs), and a note on who the data came from.
2. Circle anything missing or strange, such as a squashed axis that makes a small change look huge.
3. Write what a quick reader would believe from the graph, and what the numbers actually show.
4. Redraw one graph honestly on squared paper.

How you'll know: Your makeover tells the same data story without exaggerating it, and you can explain each change you made.

Go further: Deliberately draw a misleading version of your own data, then swap with a partner and see if they can catch the trick.

You need: a set of ten number cards (made up pocket-money amounts, one of them very large) · calculator

1. Put the cards in order and find the median, mean, mode and range.
2. Remove the outlier card and calculate them again.
3. Swap the outlier for an even bigger number. What changes, and what stays the same?
4. Write a rule in your own words about which average to use when there is an outlier.

How you'll know: Your rule matches what happened: the mean and range jump, while the median barely moves.

Go further: Find a real dataset with an outlier (house prices, rainfall in a storm, a sports score) and decide whether the outlier is a mistake or a rare real event.

You need: a normal dice · a dice with a small piece of Blu Tack stuck on one face · tally chart

1. Predict how many times each number should come up in 60 rolls of a fair dice (60 × 1/6 = 10).
2. Roll the normal dice 60 times and tally. Calculate the experimental probability of each number as a fraction and a decimal.
3. Repeat with the Blu Tack dice. Predict first: which number will come up more often, and why?
4. Pool the class results for each dice and compare them with 1/6 (about 0.17).

How you'll know: You can explain why the normal dice's results wobble around 10 each, why the pooled results sit closer to 1/6, and whether the Blu Tack dice is likely to be unfair.

Go further: Decide how many rolls you would need before you would be willing to accuse a dice of being unfair, and explain your reasoning.